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In **Pregunta 10**, you are asked to identify which of the given statements are compound propositions and formalize them. Let's analyze the options:

1. **I. Me voy al cine o sino al teatro**
   - This is a compound proposition because it combines two statements ("Me voy al cine" and "Me voy al teatro") using the disjunction "o sino".
   - Formalization: \( p \lor q \) (where \( p \) = "Me voy al cine" and \( q \) = "Me voy al teatro").

2. **II. No es cierto que Lima está en la costa**
   - This is also a compound proposition because it involves a negation of the statement "Lima está en la costa".
   - Formalization: \( \neg p \) (where \( p \) = "Lima está en la costa").

3. **III. Si me caso, entonces no seré soltero**
   - This is a conditional statement, which is also a compound proposition.
   - Formalization: \( p \rightarrow \neg q \) (where \( p \) = "Me caso" and \( q \) = "Soy soltero").

4. **IV. \(2^3 = 8\) y además \(2^4 = 16\)**
   - This is a conjunction of two mathematical statements, so it is a compound proposition.
   - Formalization: \( p \land q \) (where \( p \) = \(2^3 = 8\) and \( q \) = \(2^4 = 16\)).

5. **V. Leo el módulo y aprendo la lección**
   - This is a conjunction ("y") of two statements ("Leo el módulo" and "Aprendo la lección"), so it is a compound proposition.
   - Formalization: \( p \land q \) (where \( p \) = "Leo el módulo" and \( q \) = "Aprendo la lección").

Now, looking at the possible answers:

- a) **I; II**: This only considers the first two statements as compound, which is incorrect because the others are also compound.
- b) **I; III; IV; V**: This correctly identifies all the compound propositions.
- c) **todas**: This would be incorrect since not all statements are compound.
- d) **III; IV; V**: This leaves out the first two, which are also compound.
- e) **ninguna**: Incorrect, as some are compound.

The correct answer is **b) I; III; IV; V**.

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For **Pregunta 11**, you are asked to create the truth table for the following logical expression:

\[
\neg ((p \land q) \rightarrow q)
\]

This involves:
- \( p \land q \) (conjunction),
- \( (p \land q) \rightarrow q \) (implication),
- \( \neg ((p \land q) \rightarrow q) \) (negation of the implication).

Would you like me to solve this step by step, or is there a specific part you'd like me to focus on?

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Here are 5 related questions:

1. What is a compound proposition, and how do we formalize it in logic?
2. How does negation affect the truth value of a proposition?
3. What is the difference between a tautology and a contradiction?
4. How do conditional statements work in logical propositions?
5. Can mathematical statements be considered logical propositions? If so, how?

**Tip**: When working with logical statements, always break them down into their components to create the truth table more easily.

Identifique cuáles de los siguientes enunciados representan una proposición compuesta y formalícela.

Learn how to identify and formalize compound propositions in logic. This problem involves the use of conjunctions, disjunctions, implications, and negations, suitable for high school students studying propositional logic.

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